A Geometric Approach to Average Problems on Multinomial and Negative Multinomial Models
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School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2
Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China
3
Department of Mathematics, Duke University, Durham, NC 27708, USA
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 306; https://doi.org/10.3390/e22030306
Received: 12 February 2020
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Revised: 29 February 2020
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Accepted: 5 March 2020
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Published: 8 March 2020
(This article belongs to the Special Issue Information Geometry III)
This paper is concerned with the formulation and computation of average problems on the multinomial and negative multinomial models. It can be deduced that the multinomial and negative multinomial models admit complementary geometric structures. Firstly, we investigate these geometric structures by providing various useful pre-derived expressions of some fundamental geometric quantities, such as Fisher-Riemannian metrics, -connections and -curvatures. Then, we proceed to consider some average methods based on these geometric structures. Specifically, we study the formulation and computation of the midpoint of two points and the Karcher mean of multiple points. In conclusion, we find some parallel results for the average problems on these two complementary models.
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MDPI and ACS Style
Li, M.; Sun, H.; Li, D. A Geometric Approach to Average Problems on Multinomial and Negative Multinomial Models. Entropy 2020, 22, 306. https://doi.org/10.3390/e22030306
AMA Style
Li M, Sun H, Li D. A Geometric Approach to Average Problems on Multinomial and Negative Multinomial Models. Entropy. 2020; 22(3):306. https://doi.org/10.3390/e22030306
Chicago/Turabian StyleLi, Mingming, Huafei Sun, and Didong Li. 2020. "A Geometric Approach to Average Problems on Multinomial and Negative Multinomial Models" Entropy 22, no. 3: 306. https://doi.org/10.3390/e22030306
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